On Weakly H-embedded Subgroups of Finite Groups

Let G be a finite group and H a subgroup of G. We say that H is an H-subgroup in G if N-G(H) (HH)-H-g for all gG; H is called weakly H-subgroup in G if G has a normal subgroup K such that G=HK and H K is an H-subgroup in G. We say that H is weakly H -embedded in G if G has a normal subgroup K such that H-G=HK and H K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that some subgroups of prime power order are weakly H-embedded in G. Our results improve and generalize several recent results in the literature.